CN113241935A - Random PWM selective harmonic elimination method for single-phase inverter - Google Patents

Random PWM selective harmonic elimination method for single-phase inverter Download PDF

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CN113241935A
CN113241935A CN202110704463.6A CN202110704463A CN113241935A CN 113241935 A CN113241935 A CN 113241935A CN 202110704463 A CN202110704463 A CN 202110704463A CN 113241935 A CN113241935 A CN 113241935A
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inverter
pwm
random
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pulse
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CN113241935B (en
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姜国强
李国华
曹冬满
付振芳
李丰
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Liaoning Technical University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H02M1/12—Arrangements for reducing harmonics from ac input or output
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44—Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/53—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
    • H02M7/537—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters
    • H02M7/539—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters with automatic control of output wave form or frequency
    • H02M7/5395—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters with automatic control of output wave form or frequency by pulse-width modulation

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Abstract

The invention provides a random PWM selective harmonic elimination method for a single-phase inverter, and relates to the technical field of pulse width modulation of the single-phase inverter. The method places the PWM voltage pulse at the rear side of the switching period, thereby simplifying the switching period Tn+1The calculation formula of (2) does not need to calculate the duty ratio D any moren+1Solve the parameter Tn+1And Dn+1Contradiction of mutual restriction; on the basis, 2 random PWM selective harmonic wave elimination method ideas are summarized, and a general formula of a switching period, an effective random number k and a corresponding switching frequency extreme value is deduced. The method can realize the frequency spectrum shaping of the output voltage of the inverter under the condition of not adding a digital filter, and has the characteristics of simple algorithm, small calculated amount and easy realization.

Description

Random PWM selective harmonic elimination method for single-phase inverter
Technical Field
The invention relates to the technical field of pulse width modulation of single-phase inverters, in particular to a random PWM selective harmonic elimination method for a single-phase inverter.
Background
The Random Pulse Width Modulation (RPWM) strategy is an effective method for suppressing electromagnetic interference of power electronic converters, and electromagnetic vibration and noise of loads. As shown in fig. 1, RPWM can be classified according to the randomness of pulse positions: random lead-lag, random zero vector distribution modulation, random displacement of pulse center, random pulse position modulation, random phase shift pulse width modulation, variable delay random pulse width modulation, asymmetric carrier random pulse width modulation, single random pulse position, fractal space vector modulation and the like. However, the conventional RPWM strategy can only uniformly disperse the harmonic power peak in the power spectrum within a certain frequency range, and cannot selectively inhibit special subharmonics; for example, the resonant frequency of a load such as a motor.
In order to realize single-phase inverter output voltage spectrum shaping in an RPWM strategy, harmonic power in a specified frequency range can be reduced by utilizing a low-pass filter and a band-pass filter, but the method is relatively complex, and the calculation amount of the low-pass and band-pass digital filters is large; and the harmonics in the designated frequency range are not completely eliminated, but the frequency band is avoided in the random spreading process, namely, the harmonic content in the frequency band is not increased on the original basis.
The literature, namely a random space vector pulse width modulation selective voltage harmonic elimination method for a three-phase inverter, provides a random PWM selective harmonic elimination method, and specific subfrequency harmonics are eliminated selectively in the Fourier series of the output voltage of the inverter by utilizing a mode that front and back terms are mutually counteracted; in theory, certain subharmonics can be eliminated completely. The idea is to realize selective voltage harmonic elimination in a random PWM strategy, mainly aiming at higher harmonics; while the common SHEPWM mainly aims at 5,7 and other low-order harmonics, the two methods do not belong to the same method. But in this method the switching period T isn+1The calculation formula of (2) is relatively complex; and it is necessary to first calculate the duty ratio Dn+1. Due to Dn+1Calculation of the point position instant in a switching cycle, resulting in Tn+1And Dn+1Are mutually conditional, thereby presenting difficulties for the specific implementation of the method.
Disclosure of Invention
The technical problem to be solved by the present invention is to provide a method for eliminating random PWM selective harmonics of a single-phase inverter, which realizes selective elimination of specific subharmonics on the basis of realizing the basic function of a random PWM strategy of the single-phase inverter.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: the random PWM selective harmonic elimination method for the single-phase inverter comprises the following steps:
step 1, the inverter output PWM voltage pulse is arranged at the rear side of the switching period, and the switching period T of the inverter is simplifiedn+1No longer calculating the duty ratio Dn+1；
Placing the PWM voltage pulse at the rear side of the switching period; the PWM voltage pulse is regarded as the output voltage u of the single-phase voltage type inverterABAnd the DC side voltage V of the inverterdcSum of where VdcIs a constant; if the PWM voltage pulse frequency spectrum does not contain the specific subharmonic frequency f0Output voltage u of single-phase voltage type inverterABThe subharmonic is not contained in the frequency spectrum;
the expression of the nth period of the PWM voltage pulse is shown as the following formula:
Figure BDA0003130602990000021
therefore, the expression of the PWM voltage pulse is as follows:
Figure BDA0003130602990000022
wherein, gn(t) represents PWM voltage pulses of the nth pulse period, g (t) represents PWM voltage pulses, A represents the high level of the PWM voltage pulses, DnIs the duty cycle of the nth period, TnIs the period of the nth pulse, tn、tn+1Respectively the start time of the nth and the (N + 1) th pulse periods, wherein N is the period number of the PWM voltage pulse;
performing fourier transform on the expression of the PWM voltage pulse:
Figure BDA0003130602990000023
wherein G (f) is the Fourier transform of the pulse sequence g (t), f is the frequency, ω is the angular frequency, and j represents the imaginary part of the Fourier transform;
setting c (f)0) For the general form of the real and imaginary parts in the fourier transform described above, the following equation is shown:
Figure BDA0003130602990000024
wherein f is0For the frequency of the harmonics to be cancelled,
Figure BDA0003130602990000025
is the initial phase angle of sin ();
step 2, on the basis of the step 1, obtaining two methods for random PWM selective harmonic elimination, and calculating the switching period of the inverter, the effective random number k and the extreme value of the corresponding switching frequency;
substituting the expression of PWM voltage pulse into c (f)0) The expression of (a) is given by:
Figure BDA0003130602990000026
wherein m is the sequence number of the PWM voltage pulse;
in the above-mentioned c (f)0) On the basis of the expression, two random PWM selective harmonic elimination methods are obtained, which specifically comprise the following steps:
the method comprises the following steps: using the above c (f)0) The second summation subentry of the m + e term in the expression summation terms offsets the first summation subentry of the m term; offsetting the first summation component of the m +1 th term by using the second summation component of the m + e +1 th term; and so on; wherein, the summation sub-term refers to c (f)0) One item of the integral calculation result of each pulse in the expression is shown, m is the sequence number of the pulse, and e is a positive integer;
the method 2 comprises the following steps: using c (f)0) The first summation subentry of the m + e term in the expression summation terms offsets the second summation subentry of the m term; offsetting a second summation element of the m +1 term by using the first summation element of the m + e +1 term; and so on;
c (f) by method 10) The following formulas (6) to (9) are obtained by simplifying and calculating the calculation formula:
Figure BDA0003130602990000031
Figure BDA0003130602990000032
Figure BDA0003130602990000033
Figure BDA0003130602990000034
wherein, tn+e+1Is the start time of the (n + e + 1) th pulse period, k is a random integer, Tn+1、Tn+2The periods of the (n + 1) th and (n + 2) th pulses, respectively;
by Tn+1Given the frequency f of the subharmonic to be eliminated0Obtaining the maximum value k of the random integer k on the premise of the limit value of the duty ratio and the switching periodmaxAnd the minimum value kminThe following formula shows:
Figure BDA0003130602990000035
wherein D ismaxAnd DminDuty cycle maximum and minimum values; f. ofmaxAnd fminThe method comprises the steps of setting the maximum value and the minimum value of instantaneous switching frequency of an inverter in advance;
then each kmin～kmaxMaximum value f of instantaneous switching frequency of inverter corresponding to positive integer k within rangekmaxAnd minimum value fkminAs shown in the following equation:
Figure BDA0003130602990000041
in the formula (f)kmaxAnd fkminThe maximum value and the minimum value of the inverter switching frequency corresponding to the positive integer k;
from the above formula, the random integers k and fkmaxAnd fkminInversely proportional, i.e., the switching frequency of the inverter decreases with increasing k or increases with decreasing k;
by method 2 on c (f)0) The calculation formula is simplified and calculated to obtain the following formula:
Figure BDA0003130602990000042
Figure BDA0003130602990000043
Figure BDA0003130602990000044
Figure BDA0003130602990000045
further obtaining the maximum value k of the random integer kmaxAnd the minimum value kminEach k ofmin～kmaxMaximum value f of instantaneous switching frequency of inverter corresponding to positive integer k within rangekmaxAnd minimum value fkminThe following formula shows:
Figure BDA0003130602990000046
Figure BDA0003130602990000047
step 3, selectively eliminating harmonic waves; firstly, determining the frequency f of subharmonic to be eliminated0And maximum value f of instantaneous switching frequency of invertermaxAnd minimum value fminAnd calculating the maximum value D of the inverter duty ratio according to the preset modulation degree MmaxAnd a minimum value DminAnd then calculating to obtain the maximum value k of the random integer kmaxAnd the minimum value kminObtaining the value range of the random integer k; randomly selecting 1 k value in the value range of the random integer k; k, TnAnd DnSubstitution into Tn+1Calculating the next switching period value Tn+1(ii) a Finally, through the assignment of the comparison register in the DSP, the PWM driving signal is generated, thereby eliminating the specific subharmonic frequency f in the RPWM control0The harmonics of (b).
Adopt the produced beneficial effect of above-mentioned technical scheme to lie in: the random PWM selective harmonic elimination method of the single-phase inverter provided by the invention places the voltage PWM pulse at the rear side of the switching period, thereby simplifying the switching period Tn+1A calculation formula solves the parameter Tn+1And Dn+1Conflict of mutual restriction. Two RPWM selective harmonic elimination ideas are provided; and deducing corresponding switching period, random number and general formula of corresponding frequency extreme value, which is more convenient for parameter calculation. The method can realize the frequency spectrum shaping of the output voltage of the inverter under the condition of not adding a digital filter, and has the characteristics of simple algorithm, small calculated amount and easy realization.
Compared with the traditional fixed switching frequency SPWM strategy, the method can uniformly distribute the harmonic power peaks at the carrier frequency and integral multiples thereof in a selected frequency range. Harmonics at specific frequencies can be selectively reduced compared to conventional RPWM strategies. The method provides a new pulse position for the RPWM selective harmonic elimination method.
Drawings
FIG. 1 is a diagram of the PWM classification of random pulse positions according to the background of the invention;
FIG. 2 is a pulse sequence diagram according to an embodiment of the present invention, in which (a) the PWM pulse is located at the center of the switching period and (b) the PWM pulse is located at the rear side of the switching period;
fig. 3 is a topology diagram of a single-phase voltage-type inverter according to an embodiment of the present invention;
FIG. 4 is a flow chart of a switching cycle calculation according to an embodiment of the present invention;
FIG. 5 is a diagram of PSD simulation waveforms under different methods according to an embodiment of the present invention, where (a) is a conventional SPWM method, (b) is a conventional random SPWM method, and (c) is a method of the present invention where M is 0.9, f07kHZ and (d) is the same as 0.7, f07kHZ and (e) is obtained by the process of the invention M0.5, f0＝7kHZ；
FIG. 6 shows different M and f according to an embodiment of the present invention0Time voltage and current simulation oscillogram, wherein (a) is M-0.9, f0Voltage waveform diagram at 7kHZ, M0.9, f0Current waveform diagram at 7kHZ, M is 0.9, f is (c)0An enlarged view of the simulated waveform at 7 kHZ;
FIG. 7 shows a variation M and f provided by an embodiment of the present invention0Time voltage and current PSD experiment waveform diagram, wherein (a) is M-0.9, f0Voltage PSD waveform at 7kHZ, where M is 0.9 and f is (b)0Current PSD waveform at 7kHZ, where M is 0.9 and f is (c)0Voltage PSD waveform diagram at 9kHZ, M0.9, f0A current PSD waveform diagram at 9 kHZ;
fig. 8 is a switching frequency distribution diagram of an inverter according to an embodiment of the present invention;
FIG. 9 shows an inverter output voltage u according to an embodiment of the present inventionABAn experimental oscillogram;
FIG. 10 shows an inverter output current i according to an embodiment of the present inventionABAn experimental oscillogram;
FIG. 11 shows an inverter output voltage u according to an embodiment of the present inventionABAnd current iABThe experimental waveform is magnified.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
In this embodiment, taking an experimental prototype system of a voltage-type inverter as an example, the harmonic of the inverter is selectively eliminated by using the random PWM selective harmonic elimination method of the single-phase inverter of the present invention.
In this embodiment, the method for eliminating random PWM selective harmonics of the single-phase inverter includes the following steps:
step 1, the inverter output PWM voltage pulse is arranged at the rear side of the switching period, and the switching period T of the inverter is simplifiedn+1No longer calculating the duty ratio Dn+1；
In random PWM selective harmonic cancellation, the switching period Tn+1The calculation of the method is crucial, and the method and the corresponding pulse position in the literature "three-phase inverter random space vector pulse width modulation selective voltage harmonic elimination method" are shown in the following formula and fig. 2 (a).
Figure BDA0003130602990000061
Wherein D isnAnd Dn+1Duty cycles for the nth and n +1 switching periods; k is an effective random number; f. of0Is the frequency to be eliminated; t isnIs the nth switching period value.
Calculating T in the formulan+1First, the parameter D needs to be calculatedn+1. In a sinusoidal pulse width modulation strategy, the duty cycle D is typically calculated as (1+ Msin (ω t))/2, where M is the modulation ratio. In a specific implementation process, the ω t value is usually calculated according to the corresponding moment of the midpoint position in the switching period; i.e. calculate Dn+1Time-press a switching period Tn+1And calculating the midpoint moment. Thus, at Tn+1Unknown, next switching cycle duty cycle Dn+1It cannot be calculated. And references toMore in number and relatively complex.
Therefore, the present invention places the PWM voltage pulses on the rear side of the switching period, as shown in fig. 2 (b); the PWM voltage pulse is regarded as the output voltage u of the single-phase voltage type inverter in FIG. 3ABAnd the DC side voltage V of the inverterdcSum of where VdcIs a constant; if the PWM voltage pulse frequency spectrum does not contain the specific subharmonic frequency f0Output voltage u of single-phase voltage type inverterABThe subharmonic is not contained in the frequency spectrum;
the expression of the nth period of the PWM voltage pulse is shown as the following formula:
Figure BDA0003130602990000062
therefore, the expression of the PWM voltage pulse is as follows:
Figure BDA0003130602990000063
wherein, gn(t) represents PWM voltage pulses of the nth pulse period, g (t) represents PWM voltage pulses, A represents the high level of the PWM voltage pulses, DnIs the duty cycle of the nth period, TnIs the period of the nth pulse, tn、tn+1Respectively the start time of the nth and the (N + 1) th pulse periods, wherein N is the period number of the PWM voltage pulse;
performing fourier transform on the expression of the PWM voltage pulse:
Figure BDA0003130602990000071
wherein G (f) is the Fourier transform of the pulse sequence g (t), f is the frequency, ω is the angular frequency, and j represents the imaginary part of the Fourier transform;
setting c (f)0) For the general form of the real and imaginary parts in the fourier transform described above, the following equation is shown:
Figure BDA0003130602990000072
wherein f is0For the frequency of the harmonics to be cancelled,
Figure BDA0003130602990000073
is the initial phase angle of sin ();
if c (f)0) For any angle
Figure BDA0003130602990000074
Are all equal to 0, then equation (4) is applied to the subharmonic frequency f to be eliminated0Also equal to 0, i.e. selective harmonic cancellation is achieved in the PWM voltage pulse spectrum;
step 2, on the basis of the step 1, obtaining two methods for random PWM selective harmonic elimination, and calculating the switching period of the inverter, the effective random number k and the extreme value of the corresponding switching frequency;
substituting the expression of PWM voltage pulse into c (f)0) The expression of (a) is given by:
Figure BDA0003130602990000075
wherein m is the sequence number of the PWM voltage pulse;
in the above-mentioned c (f)0) On the basis of the expression, two random PWM selective harmonic elimination methods are obtained, which specifically comprise the following steps:
the method comprises the following steps: using the above c (f)0) The second summation subentry of the m + e term in the expression summation terms offsets the first summation subentry of the m term; offsetting the first summation component of the m +1 th term by using the second summation component of the m + e +1 th term; and so on; wherein, the summation sub-term refers to c (f)0) One item of the integral calculation result of each pulse in the expression is shown, m is the sequence number of the pulse, and e is a positive integer;
the method 2 comprises the following steps: using c (f)0) The first summation element of the m + e term in the expression summation element counteracts the mA second summed sub-term of the term; offsetting a second summation element of the m +1 term by using the first summation element of the m + e +1 term; and so on;
c (f) by method 10) The following formulas (6) to (9) are obtained by simplifying and calculating the calculation formula:
Figure BDA0003130602990000081
Figure BDA0003130602990000082
Figure BDA0003130602990000083
Figure BDA0003130602990000084
wherein, tn+e+1Is the start time of the (n + e + 1) th pulse period, k is a random integer, Tn+1、Tn+2The periods of the (n + 1) th and (n + 2) th pulses, respectively;
Tn+1compared with the traditional method, the switching period T in the method is longer than that in the traditional methodn+1The calculation method is obviously simpler, and the duty ratio D of the next switching period does not need to be calculatedn+1. Thereby solving Tn+1And Dn+1The contradiction of mutual restriction is more beneficial to practical application.
By Tn+1Given the frequency f of the subharmonic to be eliminated0Obtaining the maximum value k of the random integer k on the premise of the limit value of the duty ratio and the switching periodmaxAnd the minimum value kminThe following formula shows:
Figure BDA0003130602990000085
wherein D ismaxAnd DminDuty cycle maximum and minimum values; f. ofmaxAnd fminThe method comprises the steps of setting the maximum value and the minimum value of instantaneous switching frequency of an inverter in advance;
in general, more than one positive integer k satisfies the above condition, and each kmin～kmaxMaximum value f of instantaneous switching frequency of inverter corresponding to positive integer k within rangekmaxAnd minimum value fkminAs shown in the following equation:
Figure BDA0003130602990000086
in the formula (f)kmaxAnd fkminThe maximum value and the minimum value of the inverter switching frequency corresponding to the positive integer k;
from the above formula, the random integers k and fkmaxAnd fkminInversely proportional, i.e., the switching frequency of the inverter decreases with increasing k or increases with decreasing k;
it should be noted that, when k is small, fkmaxThe result of the formula calculation may be negative, which means that the frequency f and the duty ratio D in the denominator of the formula can be set to 0 without taking limit values, and the maximum value of the frequency is + ∞.
By method 2 on c (f)0) The calculation formula is simplified and calculated to obtain the following formula:
Figure BDA0003130602990000091
Figure BDA0003130602990000092
Figure BDA0003130602990000093
Figure BDA0003130602990000094
further obtaining the maximum value k of the random integer kmaxAnd the minimum value kminEach k ofmin～kmaxMaximum value f of instantaneous switching frequency of inverter corresponding to positive integer k within rangekmaxAnd minimum value fkminThe following formula shows:
Figure BDA0003130602990000095
Figure BDA0003130602990000096
step 3, selectively eliminating harmonic waves; as shown in FIG. 4, the subharmonic frequency f to be eliminated is first determined0And maximum value f of instantaneous switching frequency of invertermaxAnd minimum value fminAnd calculating the maximum value D of the inverter duty ratio according to the preset modulation degree MmaxAnd a minimum value DminAnd then calculating to obtain the maximum value k of the random integer kmaxAnd the minimum value kminObtaining the value range of the random integer k; randomly selecting 1 k value in the value range of the random integer k; k, TnAnd DnSubstitution into Tn+1Calculating the next switching period value Tn+1(ii) a Finally, through the assignment of the comparison register in the DSP, the PWM driving signal is generated, thereby eliminating the specific subharmonic frequency f in the RPWM control0The harmonics of (b).
In the embodiment, the voltage-type inverter experimental prototype system comprises a single-phase inverter, a driving circuit, a main control chip, an oscilloscope and an electric energy quality analyzer; the output end of the single-phase inverter is connected with a resistance-inductance load, and the power switching device of the inverter is an IGBT integrated anti-parallel freewheeling diode BSM50GB120DN 2; the driving circuit adopts an IGBT integrated driving module DA962D 6; the inverter dead time is 4.27 mus; the system main control chip adopts 32-bit DSP TMS320F 2812; the oscilloscope model is DS 1052E; the electric energy quality analyzer is HIOKI PW 3198; the single phase inverter parameters are shown in table 1.
TABLE 1 parameter table for single-phase inverter
Parameter(s) Numerical value Parameter(s) Numerical value
Frequency f to be cancelled0/ kHZ 7,9 Inverter resistive load/omega 5
Upper limit of switching frequency/kHZ 8 Inverter inductive load/mH 5
Lower limit of switching frequency/kHZ 1.5 DC side voltage/V of inverter 24
In this embodiment, a single-phase inverter output voltage Power Spectrum (PSD) simulation waveform is shown in fig. 5, and a single-phase inverter output voltage and current simulation waveform is shown in fig. 6. FIG. 5(a) uses the conventional SPWM method with a fixed switching frequency of 3k Hz; it can be seen from the figure that the harmonic power is dominantTo be centered around 3 khz and integer multiples thereof. Fig. 5(b) illustrates a conventional random PWM method, and compared with the conventional fixed switching frequency SPWM method, no obvious peak appears in the power spectrum, but the conventional random PWM method cannot selectively eliminate a specific secondary frequency. FIGS. 5(c), (d) and (e) show the frequency f to be eliminated according to the method of the present invention0Is 7k Hz; the modulation ratio M is 0.9, 0.7 and 0.5 respectively; as can be seen from FIGS. 5(c), (d) and (e), the method of the present invention can significantly reduce f while achieving uniform distribution of harmonic power0And harmonic power at integer multiples thereof; the correctness of the method is proved.
The experimental waveforms of the single-phase inverter output voltage and current PSD are shown in fig. 7. As can be seen from fig. 7, at f0F in PSD experimental oscillogram of voltage and current under the conditions of 7k Hz and 9k Hz respectively0And its harmonic power around integer multiples is significantly reduced. The experimental result is basically consistent with the simulation result. From the waveforms of FIGS. 5 and 7, it can be seen that at f0And within about several hundred hertz around the integral multiple frequency, the waveform has obvious gaps. This is because when f0When the harmonic power is completely eliminated, and0the close frequency is reduced by a certain amplitude; and a distance f0The more recent, the greater the magnitude of the attenuation. The characteristics can overcome the influence brought by system errors.
At f0The distribution of the inverter switching frequency percentage at 7k Hz and M of 0.9 is shown in fig. 8, where the solid line is k randomly chosen among all the available random numbers; the dotted line is the random choice of k only among the smallest 3 valid random numbers. As can be seen from the solid line in the figure, the instantaneous switching frequency can be randomly distributed in a set frequency range, and the randomness is good; the percentage distribution of the switching frequency is gradually reduced from 1.5k Hz to 8k Hz; the average switching frequency of the inverter is 2894 Hz.
As can be seen from the dashed line in the figure, when a smaller random number is selected, the instantaneous switching frequency of the inverter as a whole is increased, and the average switching frequency is increased to 3723 Hz. From the equation (10), the random integer k and the corresponding maximum value f of the switching frequencykmaxAnd minimum value fkminIs inversely proportional toWhen the average switching frequency is lower, a smaller random number k can be selected to improve the average switching frequency; an increase in current ripple due to too low a switching frequency is prevented. When the average switching frequency is higher, a larger random number k is selected to lower the average switching frequency. And f0The larger the selectable effective random number, the larger the range over which the average switching frequency can be controlled.
At f0Experimental waveforms of inverter output voltage and current at 7k Hz and M0.9 and enlarged views of the experimental waveforms are shown in fig. 9-11. As can be seen, the voltage pulse width in each switching period varies randomly, subject to the effect of the effective random number k and the duty cycle. The inverter current waveform changes in a sinusoidal manner. The larger the switching period, the larger the current ripple, without changing other conditions.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions and scope of the present invention as defined in the appended claims.

Claims (3)

1. A random PWM selective harmonic elimination method for a single-phase inverter is characterized by comprising the following steps: the method comprises the following steps:
step 1, the inverter output PWM voltage pulse is arranged at the rear side of the switching period, and the switching period T of the inverter is simplifiedn+1No longer calculating the duty ratio Dn+1；
Step 2, on the basis of the step 1, obtaining two methods for random PWM selective harmonic elimination, and calculating the switching period of the inverter, the effective random number k and the extreme value of the corresponding switching frequency;
step 3, selectively eliminating harmonic waves; firstly, determining the frequency f of subharmonic to be eliminated0And maximum value f of instantaneous switching frequency of invertermaxAnd minimum value fminAnd calculating the maximum value D of the inverter duty ratio according to the preset modulation degree MmaxAnd a minimum value DminAnd then calculating to obtain the maximum value k of the random integer kmaxAnd the minimum value kminObtaining the value range of the random integer k; randomly selecting 1 k value in the value range of the random integer k; the period T of the k, n pulsenAnd duty cycle D of the nth periodnSubstituting the inverter switching period Tn+1Calculating the next switching period value Tn+1(ii) a Finally, through the assignment of the comparison register in the DSP, the PWM driving signal is generated, thereby eliminating the specific subharmonic frequency f in the RPWM control0The harmonics of (b).
2. The random PWM selective harmonic cancellation method for a single-phase inverter according to claim 1, wherein: the specific method of the step 1 comprises the following steps:
placing the PWM voltage pulse at the rear side of the switching period; the PWM voltage pulse is regarded as the output voltage u of the single-phase voltage type inverterABAnd the DC side voltage V of the inverterdcSum of where VdcIs a constant; if the PWM voltage pulse frequency spectrum does not contain the specific subharmonic frequency f0Output voltage u of single-phase voltage type inverterABThe subharmonic is not contained in the frequency spectrum;
the expression of the nth period of the PWM voltage pulse is shown as the following formula:
Figure FDA0003130602980000011
therefore, the expression of the PWM voltage pulse is as follows:
Figure FDA0003130602980000012
wherein, gn(t) represents the PWM voltage pulse of the nth pulse period, g (t) represents the PWM voltage pulse, A represents the high level of the PWM voltage pulse,Dnis the duty cycle of the nth period, TnIs the period of the nth pulse, tn、tn+1Respectively the start time of the nth and the (N + 1) th pulse periods, wherein N is the period number of the PWM voltage pulse;
performing fourier transform on the expression of the PWM voltage pulse:
Figure FDA0003130602980000013
wherein G (f) is the Fourier transform of the pulse sequence g (t), f is the frequency, ω is the angular frequency, and j represents the imaginary part of the Fourier transform;
setting c (f)0) For the general form of the real and imaginary parts in the fourier transform described above, the following equation is shown:
Figure FDA0003130602980000021
wherein f is0For the frequency of the harmonics to be cancelled,
Figure FDA0003130602980000022
is the initial phase angle of sin ().
3. The random PWM selective harmonic cancellation method for a single-phase inverter according to claim 2, wherein: the specific method of the step 2 comprises the following steps:
substituting the expression of PWM voltage pulse into c (f)0) The expression of (a) is given by:
Figure FDA0003130602980000023
wherein m is the sequence number of the PWM voltage pulse;
in the above-mentioned c (f)0) On the basis of the expression, two random PWM selective harmonic elimination methods are obtained, which specifically comprise the following steps:
the method comprises the following steps: using the above c (f)0) The second summation subentry of the m + e term in the expression summation terms offsets the first summation subentry of the m term; offsetting the first summation component of the m +1 th term by using the second summation component of the m + e +1 th term; and so on; wherein, the summation sub-term refers to c (f)0) One item of the integral calculation result of each pulse in the expression is shown, m is the sequence number of the pulse, and e is a positive integer;
the method 2 comprises the following steps: using c (f)0) The first summation subentry of the m + e term in the expression summation terms offsets the second summation subentry of the m term; offsetting a second summation element of the m +1 term by using the first summation element of the m + e +1 term; and so on;
c (f) by method 10) The following formulas (6) to (9) are obtained by simplifying and calculating the calculation formula:
Figure FDA0003130602980000024
Figure FDA0003130602980000025
Figure FDA0003130602980000026
Figure FDA0003130602980000027
wherein, tn+e+1Is the start time of the (n + e + 1) th pulse period, k is a random integer, Tn+1、Tn+2The periods of the (n + 1) th and (n + 2) th pulses, respectively;
by Tn+1Given the frequency f of the subharmonic to be eliminated0Obtaining the maximum value k of the random integer k on the premise of the limit value of the duty ratio and the switching periodmaxAnd the minimum value kminThe following formula shows:
Figure FDA0003130602980000031
wherein D ismaxAnd DminDuty cycle maximum and minimum values; f. ofmaxAnd fminThe method comprises the steps of setting the maximum value and the minimum value of instantaneous switching frequency of an inverter in advance;
then each kmin～kmaxMaximum value f of instantaneous switching frequency of inverter corresponding to positive integer k within rangekmaxAnd minimum value fkminAs shown in the following equation:
Figure FDA0003130602980000032
in the formula (f)kmaxAnd fkminThe maximum value and the minimum value of the inverter switching frequency corresponding to the positive integer k;
from the above formula, the random integers k and fkmaxAnd fkminInversely proportional, i.e., the switching frequency of the inverter decreases with increasing k or increases with decreasing k;
by method 2 on c (f)0) The calculation formula is simplified and calculated to obtain the following formula:
Figure FDA0003130602980000033
Figure FDA0003130602980000034
Figure FDA0003130602980000035
Figure FDA0003130602980000036
further obtaining the maximum value k of the random integer kmaxAnd the minimum value kminEach k ofmin～kmaxMaximum value f of instantaneous switching frequency of inverter corresponding to positive integer k within rangekmaxAnd minimum value fkminThe following formula shows:
Figure FDA0003130602980000041
Figure FDA0003130602980000042
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